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Kerimcan OzcanMNGT 379 Operations Research2 PERT/CPM PERT Program Evaluation and Review Technique Developed by U.S. Navy for Polaris missile project Developed to handle uncertain activity times CPM Critical Path Method Developed by Du Pont & Remington Rand Developed for industrial projects for which activity times generally were known Todays project management software packages have combined the best features of both approaches. PERT and CPM have been used to plan, schedule, and control a wide variety of projects: R&D of new products and processes Construction of buildings and highways Maintenance of large and complex equipment Design and installation of new systems

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Kerimcan OzcanMNGT 379 Operations Research3 PERT/CPM PERT/CPM is used to plan the scheduling of individual activities that make up a project. Projects may have as many as several thousand activities. A complicating factor in carrying out the activities is that some activities depend on the completion of other activities before they can be started. Project managers rely on PERT/CPM to help them answer questions such as: What is the total time to complete the project? What are the scheduled start and finish dates for each specific activity? Which activities are critical and must be completed exactly as scheduled to keep the project on schedule? How long can noncritical activities be delayed before they cause an increase in the project completion time?

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Kerimcan OzcanMNGT 379 Operations Research4 Project Network A project network can be constructed to model the precedence of the activities. The nodes of the network represent the activities. The arcs of the network reflect the precedence relationships of the activities. A critical path for the network is a path consisting of activities with zero slack.

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Kerimcan OzcanMNGT 379 Operations Research5 Example: Franks Fine Floats Frank s Fine Floats is in the business of building elaborate parade floats. Frank and his crew have a new float to build and want to use PERT/CPM to help them manage the project. The table below shows the activities that comprise the project. Each activitys estimated completion time (in days) and immediate predecessors are listed as well. Frank wants to know the total time to complete the project, which activities are critical, and the earliest and latest start and finish dates for each activity.

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Kerimcan OzcanMNGT 379 Operations Research7 Earliest Start and Finish Times Step 1: Make a forward pass through the network as follows: For each activity i beginning at the Start node, compute: Earliest Start Time = the maximum of the earliest finish times of all activities immediately preceding activity i. (This is 0 for an activity with no predecessors.) Earliest Finish Time = (Earliest Start Time) + (Time to complete activity i ). The project completion time is the maximum of the Earliest Finish Times at the Finish node. Start Finish B 3 D 3 A 3 C 2 G 6 F 3 H 2 E

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Kerimcan OzcanMNGT 379 Operations Research8 Latest Start and Finish Times Step 2: Make a backwards pass through the network as follows: Move sequentially backwards from the Finish node to the Start node. At a given node, j, consider all activities ending at node j. For each of these activities, i, compute: Latest Finish Time = the minimum of the latest start times beginning at node j. (For node N, this is the project completion time.) Latest Start Time = (Latest Finish Time) - (Time to complete activity i ). Start Finish B 3 D 3 A 3 C 2 G 6 F 3 H 2 E

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Kerimcan OzcanMNGT 379 Operations Research12 Example: EarthMover, Inc. Earliest/Latest Times Activity ES EF LS LF Slack A * B * C D E F * G * H I * Crashing The completion time for this project using normal times is 30 weeks. Which activities should be crashed, and by how many weeks, in order for the project to be completed in 26 weeks?

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Kerimcan OzcanMNGT 379 Operations Research13 Crashing Activity Times In the Critical Path Method (CPM) approach to project scheduling, it is assumed that the normal time to complete an activity, tj, which can be met at a normal cost, cj, can be crashed to a reduced time, tj, under maximum crashing for an increased cost, cj. Using CPM, activity j's maximum time reduction, Mj, may be calculated by: Mj = tj - tj'. It is assumed that its cost per unit reduction, Kj, is linear and can be calculated by: Kj = (cj' - cj)/Mj.